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2 years ago

Which set contains only whole numbers divisible to 6?

1 answer:

7 0

Only <span>set Y = {6, 24, 36, 78, 84}, contains only whole numbers divisible by 6.

There were no options but this was the answer to this question on a quiz.

hope this helps!</span>

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Prove the following by induction. In each case, n is apositive integer.<br> 2^n ≤ 2^n+1 - 2^n-1 -1.

frutty [35]

<h2>Answer with explanation:</h2>

We are asked to prove by the method of mathematical induction that:

$2^n\leq 2^{n+1}-2^{n-1}-1$

where n is a positive integer.

Let us take n=1

then we have:

$2^1\leq 2^{1+1}-2^{1-1}-1\\\\i.e.\\\\2\leq 2^2-2^{0}-1\\\\i.e.\\2\leq 4-1-1\\\\i.e.\\\\2\leq 4-2\\\\i.e.\\\\2\leq 2$

Hence, the result is true for n=1.

Let us assume that the result is true for n=k

i.e.

$2^k\leq 2^{k+1}-2^{k-1}-1$

Now, we have to prove the result for n=k+1

i.e.

<u>To prove:</u> $2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1$

Let us take n=k+1

Hence, we have:

$2^{k+1}=2^k\cdot 2\\\\i.e.\\\\2^{k+1}\leq 2\cdot (2^{k+1}-2^{k-1}-1)$

( Since, the result was true for n=k )

Hence, we have:

$2^{k+1}\leq 2^{k+1}\cdot 2-2^{k-1}\cdot 2-2\cdot 1\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{k-1+1}-2\\\\i.e.\\\\2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-2$

Also, we know that:

$-2$

(

Since, for n=k+1 being a positive integer we have:

$2^{(k+1)+1}-2^{(k+1)-1}>0$ )

Hence, we have finally,

$2^{k+1}\leq 2^{(k+1)+1}-2^{(k+1)-1}-1$

Hence, the result holds true for n=k+1

Hence, we may infer that the result is true for all n belonging to positive integer.

i.e.

$2^n\leq 2^{n+1}-2^{n-1}-1$ where n is a positive integer.

6 0

2 years ago

Which of the following is a Riemann Sum used to estimate?

fgiga [73]

Answer:

A. Area under a curve

Step-by-step explanation:

Edge 2021

5 0

2 years ago

An online ticket seller charges $44 for each ticket ton concert, plus a fixed handling fee of $12. Define the unknown variables

enot [183]

Answer:

x= number of tickets bought

y= total

44x+12=y

8 0

2 years ago

-7(n+3)-8(1+8n)<br>Find answer

Oxana [17]

-7n-21-8-64n distributive property -7n-64n-29 commutative property -51n-29 combine like terms

4 0

2 years ago

Read 2 more answers

State whether the given measurements determine zero, one, or two triangles.

ohaa [14]

Answer:

One

Step-by-step explanation:

Find the value of B

Applying the law of sines

$\frac{a}{sin(A)}$ = $\frac{b}{sin(B)}$

substitute the given values

$\frac{23}{sin(61)}$ = $\frac{24}{sin(B)}$

sin (B) = $\frac{24}{23}$ Sin(61)

step 2

Find the measure of angle C

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

61 + 65.87 + C = 180

C = 53.13

step 3

Find the value of c

Applying the law of sines

$\frac{a}{sin(A)}$ = $\frac{c}{sin(C)}$

substitute the given values

$\frac{23}{sin(61)}$ = $\frac{c}{sin(53.13)}$

c = $\frac{23}{sin(61)}$ SIN (53.13)

C=21.04 units

there can only be one value for each measurement, therefore there can only be one triangle

4 0

2 years ago